ON REGULAR COVERINGS OF 3-MANIFOLDS BY HOMOLOGY 3-SPHERES

We study homology 3-spheres M approximately that admit fixed point free actions by a finite group G. If G also admits a fixed point free orthogonal action on S3 and if certain projective Z[G]-modules satisfy a cancellation property we show that the regular covering M approximately --> M approximately/G is induced from a standard regular covering S3 --> S3/G by means of a map f: M approximately/G --> S3/G whose degree is relatively prime to the order of G (Theorem 1). We also completely characterize those regular coverings M approximately --> M where M is Seifert fibered (sectional sign 4). Finally, starting with any given regular covering M approximately 0 --> M0 with group of covering transformations G, M0 irreducible, and M approximately 0 a homology 3-sphere, we show how to construct another regular covering M approximately --> M with M approximately a homology 3-sphere and the same group G of covering trans formations, with M sufficiently large, M and M0 not homotopy equivalent, and a degree 1 map f: M --> M0 that induces the regular covering M approximately - M from the regular covering M aproximately --> M0.